Mathematical Sciences: Vortices in Algebraic and Symplectic Geometry

数学科学：代数和辛几何中的涡旋

• 批准号: 9303545
• 负责人: Steven Bradlow
• 金额: $ 4.02万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303545&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Vortices; Algebraic; Symplectic

This award supports research in the area of vortices in algebraic and symplectic geometry. It is based on earlier work by the investigator on vortices and stable holomorphic pairs. Vortices are minima of Yang-Mills-Higgs energy, and holomorphic pairs are holomorphic vector bundles with prescribed holomorphic sections. This research concerns new directions in the study of vortices and stable pairs and involves a generalization of the notion of a pair to that of a triple consisting of two holomorphic bundles together with a holomorphic bundle homomorphism. This will address the way in which objects can be obtained by a dimensional reduction of an equivariant stable bundle on the Cartesian product of the Riemann surface with the projective line. This award is in the general area of geometry and, in particular, in algebraic and symplectic geometry. This research will aid in our understanding of 4-dimensional manifolds and are central to the current research in 'gauge theory'. In lay terms, a 'manifold' plays the role of a surface.

该奖项支持代数和符号几何形状涡流领域的研究。 它基于研究人员对涡旋和稳定的全态对的早期工作。 涡旋是杨米尔斯·希格斯（Yang-Mills-Higgs）能量的最小值，而全体形态对是带有全体形态切片的圆形载体束。 这项研究涉及涡旋和稳定对研究中的新方向，并涉及一对概念的概括，该概念与三个圆锥形捆绑包一起的三重概念以及全体形态束同构的概念。 这将解决通过用投影线的笛卡尔表面上的笛卡尔产物上的模棱两可的稳定束来获得对象的方式。 该奖项是在几何形状的一般领域，尤其是在代数和符号几何形状中。 这项研究将有助于我们理解四维流形，并且是当前“量规理论”研究的核心。 简而言之，“流形”起着表面的作用。